Apparatus, systems and methods for generating voltage excitation waveforms

ABSTRACT

A method described herein includes describing a load current with a discrete time function. The method includes using a first frequency and a second frequency to provide an approximation of the described load current, wherein a transform applied to the discrete time function identifies the first frequency and the second frequency. The method includes estimating a loop inductance and a loop resistance of a wire loop by exciting a transmit circuit with a voltage reference step waveform, wherein the transmit circuit includes the wire loop. The method includes scaling the approximated load current to a level sufficient to generate a minimum receive voltage signal in a receiver at a first distance between the wire loop and the receiver. The method includes generating a first voltage signal using the scaled load current, estimated loop inductance, and estimated loop resistance. The method includes exciting the transmit circuit with the first voltage signal.

CROSS REFERENCE TO RELAYED APPLICATIONS

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STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

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THE NAMES OF THE PARTIES TO A JOINT RESEARCH AGREEMENT

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BACKGROUND

Apparatus, systems and methods are described herein for providingcertain properties in transmit waveforms for use by a companion receiverin determining direction of approach relative to a transmitting source.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 shows the components of a transmit circuit, under an embodiment.

FIG. 2 shows the components of a receive circuit, under an embodiment.

FIG. 3 shows time varying magnetic flux density generated by a currentin a long wire, under an embodiment.

FIG. 4 shows time varying magnetic flux density generated by a currentin a multi-turn air core loop, under an embodiment.

FIG. 5 shows time varying magnetic flux density generated by a currentin a multi-turn ferrite core loop, under an embodiment.

FIG. 6 shows a loop antenna, under an embodiment.

FIGS. 7A-7C demonstrates excitation characteristics for a dominantlyinductive wire load, under an embodiment.

FIGS. 8A-8C demonstrates excitation characteristics for a dominantlyinductive wire load, under an embodiment.

FIGS. 9A-9C demonstrate excitation characteristics for a for adominantly resistive long wire load, under an embodiment.

FIGS. 10A-10C demonstrate excitation characteristics for a for adominantly resistive long wire load, under an embodiment.

FIG. 11 shows reference current I_(L) (t) resulting from the discretetime function I_(L)(nΔt), under an embodiment.

FIG. 12 shows phasor Φ(nΔt) rotating about a unit circle, under anembodiment.

FIG. 13 shows the frequency content of a desired current provided by adiscrete time function, under an embodiment.

FIG. 14 shows a first carrier component of a desired current, under anembodiment.

FIG. 15 shows a second carrier component of a desired current, under anembodiment.

FIG. 16 shows a two carrier approximation of a desired current, under anembodiment.

FIG. 17 shows voltage amplitudes V_(out) and V_(C) as a function oftime(seconds), under an embodiment.

FIG. 18 shows a transmit circuit, under an embodiment.

FIG. 19 shows a voltage step waveform, under an embodiment.

FIG. 20 shows a voltage signal resulting from a voltage step waveform,under an embodiment.

FIG. 21 shows a graph of an impedance vector, under an embodiment.

FIG. 22 shows a voltage signal generated by the transmit circuit, underan embodiment.

FIG. 23 shows a graph of an impedance vector, under an embodiment.

FIG. 24 shows a graph of an impedance vector, under an embodiment.

FIG. 25 shows a graph of an impedance vector, under an embodiment.

DETAILED DESCRIPTION

An electronic animal containment system is described withdirection-of-approach determination, or direction-sensitivecapabilities. The direction-sensitive animal containment systemgenerally contains a transmitter unit connected to a wire loop boundinga containment area and a receiver unit carried by the animal. Thetransmit unit provides certain properties in transmit waveforms for useby a companion receiver in determining direction of approach relative tothe wire loop bounding the containment area.

Multiple embodiments of an electronic animal containment system providevarying methods for generating the required current in the wire loop.Under one embodiment, a containment signal generator may convert anuneven duty cycle square wave into an asymmetric triangle wave. Underanother embodiment, a containment signal generator includes a discretetriangle wave generator allowing the adjustment of the rising andfalling slopes. Under this embodiment, the discrete triangle wavegenerator directly drives the output current drivers and provides twoamplitude levels for the triangle waveform.

Under either embodiment, the circuit parameters, L_(total) and R_(total)determine the generating signal required to produce the desired currentby the equation:

$\begin{matrix}{{V_{generator}(t)} = {{R_{total}*{I_{desired}(t)}} + {L_{total}*\frac{{dl}_{desired}(t)}{dt}}}} & (1)\end{matrix}$A companion receiver is responsive to:V _(receive)(t)=K _(Rx) *dβ/dt  (2)where

dβ/dt is the rate of change of the magnetic flux density; dβ/dt isdependent upon dI(t)/dtK _(Rx) =n*A*u _(c−Rx)

n=number of turns in the receive core

A=area of the receive core (m²)

U_(c−Rx)=geometry dependent relative permeability of the receive core

Under one embodiment of an electronic animal containment system, acontainment signal generator produces an uneven duty cycle square wave.A long wire load (or perimeter boundary wire) connected to thetransmitter may result in an asymmetric triangle current flowing throughthe wire. This is true when the load is predominantly inductive under anembodiment, hence:

$\begin{matrix}{{V_{generator}(t)} = {L_{total}*\frac{{dI}_{desired}(t)}{dt}}} & (3) \\{\frac{{dI}_{desired}(t)}{dt} = {{V_{generator}(t)}/L_{total}}} & (4)\end{matrix}$Under this specific condition, an uneven duty cycle square wave willproduce the desired asymmetry in the wire current.

Under another embodiment, a containment signal generator includes adiscrete triangle wave generator allowing the adjustment of the risingand falling slopes. The discrete triangle wave generator directly drivesthe output current drivers and provides two amplitude levels for thetriangle waveform. However, the desired asymmetry is produced only whenthe load is predominantly resistive under an embodiment, hence:V _(generator)(t)=R _(total) *I _(desired)(t)  (5)I _(desired)(t)=V _(generator)(t)/R _(total)  (5)Under this specific condition a discrete triangle wave generator withadjustable rising and falling slopes produce the desired asymmetry.Magnetic Field Relationships between the Transmitter and ReceiverSystem Model

FIG. 1 shows the components of a transmit circuit 100. FIG. 1 shows asignal generator 102 connected to an amplifier 120. The amplifier isconnected to transmit components comprising resistor R_(series) 104,which is in series with inductor L_(Loop) 106, which is in series withresistor R_(Loop) 108, which is in series with resistor R_(sense) 110.The transmit components are indicated in bold as shown in FIG. 1.Current I_(L) (t) 112 flows through the transmit components. Theamplifier 120 may be any amplifier topology with sufficient power outputcapability to produce V_(out)(t) and I_(L) (t) for the given load. Notethat V_(out)(t) is given by the following equation:V _(out)(t)=(R _(series) +R _(Loop) +R _(sense))*I _(L)(t)+L _(Loop) *dI_(L)(t)/dt.  (7)

FIG. 1 also shows analog-to-digital convertors 114 and 116 respectivelyconnected to the transmit loop at points 118 and 120. Ananalog-to-digital converter (ADC) is a device that converts a continuousphysical quantity (in this case, I_(L)(t) produces a voltage acrossR_(sense)) to a digital number that represents the quantity's amplitude.The conversion involves quantization of the input, so it necessarilyintroduces a small amount of error. Furthermore, instead of continuouslyperforming the conversion, an ADC does the conversion periodically,sampling the input. The result is a sequence of digital values that havebeen converted from a continuous-time and continuous-amplitude analogsignal to a discrete-time and discrete-amplitude digital signal. Thesummation component 120 of the transmit circuit combines the voltageamplitude at point 118 and point 120 to approximate the voltage dropacross R_(sense), i.e. V_(C)(t) 124.

FIG. 2 shows the components of a receive circuit 200. FIG. 2 showsinterference 202 and time varying magnetic flux density,

$\frac{d\;\beta}{dt},$204 presented to the receive components. V_(sensor)(t) 206 is thevoltage rendered by the receive R-L-C circuit. The receive componentsinclude inductor L_(s) 208 and resistor R_(s) 210 in series. The receivecomponents are in parallel with resistor R_(L) 212 and capacitor C_(RES)214 which are in series with each other. The parallel circuit componentsare also in series with capacitor C 216. Points 220 and 222 representrespective inputs for Z Amplifier 230, Y Amplifier 240, and X Amplifier250. VZ_(Receive)(t) 260 represents the output voltage of the ZAmplifier. VY_(Receive)(t) 270 represents the output voltage of the YAmplifier. VX_(Receive)(t) 280 represents the output voltage of the XAmplifier. Typically, the inductors, Ls, associated with each amplifiercircuit (X, Y, and Z) are oriented orthogonal to one another. Note thatfor the sake of simplicity, the systems and methods described belowrefer to a single amplifier of a receiver. V_(Rx sensor)(t) indicatesthe amplifier input voltage under an embodiment. V_(Receive)(t)represents amplifier output voltage.Magnetic Field Relationships

FIG. 3 shows the time varying magnetic flux density generated by acurrent in a long wire. FIG. 3 shows an inductor L_(L) 302 in serieswith a resistor R_(L) 304 which reflect the circuit model for a longwire under an embodiment. FIG. 3 shows current I_(L) 306. The point x308 represents the distance to the wire in meters. The point X 310 showsthe magnetic flux density travelling into the page. The time varyingmagnetic flux density is governed by the following equations:

$u_{0} = {4\pi*10^{- 7}( \frac{Henry}{meter} )}$I(t) = loop  current  (amps) x = distance  to  point  (meters)${\beta(t)} = {{I_{L}(t)}( \frac{u_{0}}{2\pi\; x} )}$The time varying flux density at point x is specifically given bydβ/dt=dI _(L)(t)/dt*(u ₀/2πx)  (8)

FIG. 4 shows time varying magnetic flux density generated by a currentin a multi-turn air core loop. FIG. 4 shows the direction of the timevarying magnetic flux density 402. The multi-turn air core loop 404comprises n turns, n_(L). Current I_(L) enters the page at points 408and exits the page at points 406. The coil 404, i.e. each loop turn,comprises a radius r_(L) 410. The time varying magnetic flux density ata point x along the coil axis shown is governed by the followingequations:

$\beta = {{I(t)}*n_{L}*u_{0}*{r_{L}^{2}/( {2( {r_{L}^{2} + x^{2}} )^{\frac{3}{2}}} )}}$${d\;{\beta/{dt}}} = {{{{dI}(t)}/{dt}}*n_{L}*u_{0}*{r_{L}^{2}/( {2( {r_{L}^{2} + x^{2}} )^{\frac{3}{2}}} )}}$I_(L)(t) = loop  current  (amps)$u_{0} = {4\pi*10^{- 7}( \frac{Henry}{meter} )}$n_(L) = number  of  turnsThe time varying flux density at point x along the coil axis isspecifically given by

$\begin{matrix}{{d\;{\beta/{dt}}} = {{{{dI}(t)}/{dt}}*n_{L}*u_{0}*{r_{L}^{2}/( {2( {r_{L}^{2} + x^{2}} )^{\frac{3}{2}}} )}}} & (9)\end{matrix}$

FIG. 5 shows time varying magnetic flux density 502 generated by acurrent in a multi-turn ferrite core loop 504. The ferrite core loopcomprises n turns, n_(L) 506. The coil 504, i.e. each loop turn,comprises a radius r_(L) 508. FIG. 5 shows the direction of the timevarying magnetic flux density 502 and direction of current I_(C) 510.The time varying magnetic flux density at a point x along the coil axisis governed by the following equations:

$\beta = {{I(t)}*u_{c - {Tx}}*n_{L}*u_{0}*{r_{L}^{2}/( {2( {r_{L}^{2} + x^{2}} )^{\frac{3}{2}}} )}}$${d\;{\beta/{dt}}} = {{{{dI}(t)}/{dt}}*u_{c - {Tx}}*n_{L}*u_{0}*{r_{L}^{2}/( {2( {r_{L}^{2} + x^{2}} )^{\frac{3}{2}}} )}}$I_(L)(t) = loop  current  (amps)$u_{0} = {4\pi*10^{- 7}( \frac{Henry}{meter} )}$u_(c − Tx) = 10  to  100  (typical  relative  permeability  of  the  ferritetransmitter  core  geometry  and  material)n_(L) = number  of  turnsThe time varying flux density at point x along the coil axis isspecifically given by

$\begin{matrix}{{d\;{\beta/{dt}}} = {{{{dI}_{L}(t)}/{dt}}*u_{c - {Tx}}*n_{L}*u_{0}*{r_{L}^{2}/( {2( {r_{L}^{2} + x^{2}} )^{\frac{3}{2}}} )}}} & (10)\end{matrix}$Receiver Output Voltage

Receive sensor output voltage results from proximity to a time varyingmagnetic flux density. FIG. 6 show an “n” turn 602 loop antenna 604 witharea “A” 608. Note that the area A represents the area of one loopantenna turn. The upwardly directed arrows represent time varyingmagnetic flux density 610. The parameter a 620 represents the anglebetween horizontal line 622 and the loop antenna. The receive sensoroutput voltage is given by

$V_{out} = {{{- {nx}}\frac{d\;\phi}{dt}} = {{- n}*{A({dot})}d\;{\beta/{dt}}}}$${{for}\mspace{14mu}{air}\mspace{14mu}{core}\text{:}\mspace{14mu}\frac{d\;\beta_{air}}{dt}} = \frac{u_{0}{dH}}{dt}$${{for}\mspace{14mu}{ferrite}\mspace{14mu}{core}\text{:}\mspace{14mu}\frac{d\;\beta_{FC}}{dt}} = {{u_{0}*{u_{C - {Rx}}( \frac{dH}{dt} )}} = {u_{c - {Rx}}*d\;{\beta_{air}/{dt}}}}$u_(c − Rx) = u_(r)/(1 + N(u_(r) − 1))Note that N is a geometry dependent demagnetizing factor, and u_(r) isthe relative permeability of the receive core. A small N results inu_(c−Rx) that approaches u_(r).

This particular receiver sensor output voltage, V_(Rx Sensor) (t) isgiven by:

$\begin{matrix}{{V_{{Rx}\mspace{11mu}{Sensor}}(t)} = {( {{- n}*A*u_{c - {Rx}}} )*\frac{d\;\beta}{dt}}} & (11) \\{{V_{{Rx}\mspace{11mu}{Sensor}}(t)} = {K_{Rx}*d\;{\beta/{dt}}}} & (12)\end{matrix}$where,

K_(Rx)=−n*A*u_((C−Rx))(constant receive terms)

n=number of turns in the receive core

A=area of the receive core (m²)

u_(C−Rx)=geometry dependent relative

permeability of the receive core

As shown above, the sensor output is proportional to dβ(t)/dt. However,dβ(t)/dt is dependent on the source of the time varying magnetic field(i.e. long wire, air coil, ferrite coil, etc.)

For a long wire:dβ/dt=dI _(L)(t)/dt*(u ₀/2πx)  (13)dβ/dt=dI _(L)(t)/dt*K _(Tx−long wire)  (14)where,

$u_{0} = {4\pi*10^{- 7}( \frac{Henry}{meter} )}$

x=distance to wire or loop (m)

K_(TX-long wire)=u₀/2πx

For Multi-Turn Air Core Loop:

$\begin{matrix}{{d\;{\beta/{dt}}} = {{{{dI}(t)}/{dt}}*n_{L}*u_{0}*{r_{L}^{2}/( {2( {r_{L}^{2} + x^{2}} )^{\frac{3}{2}}} )}}} & (15) \\{{d\;{\beta/{dt}}} = {{{{dI}(t)}/{dt}}*( K_{{Tx} - {{coil}\mspace{11mu}{air}}} )}} & (16)\end{matrix}$where,

n_(L)=number of turns

r_(L)=radius of the mult-turn transmit coil loop

$K_{{Tx} - {{coil}\mspace{11mu}{air}}} = {n_{L}*u_{0}*{r_{L}^{2}/( {2( {r_{L}^{2} + x^{2}} )^{\frac{3}{2}}} )}}$

For a Multi-Turn Ferrite Core Loop:

$\begin{matrix}{{d\;{\beta/{dt}}} = {{{{dI}_{L}(t)}/{dt}}*u_{c - {Tx}}*n_{L}*u_{0}*{r_{L}^{2}/( {2( {r_{L}^{2} + x^{2}} )^{\frac{3}{2}}} )}}} & (17) \\{{{d\;{\beta/{dt}}} = {{{{dI}_{L}(t)}/{dt}}*K_{{Tx} - {{coil}\mspace{11mu}{ferrite}}}}}{where}} & (18) \\{{u_{C - {Tx}} = {{geometry}\mspace{14mu}{dependent}\mspace{14mu}{relative}\mspace{14mu}{permeability}\mspace{14mu}{of}\mspace{14mu}{the}}}\text{}{{transmit}\mspace{14mu}{core}}} & (19) \\{K_{{Tx} - {{coil}\mspace{11mu}{ferrite}}} = {u_{c - {Tx}}*n_{L}*u_{0}*{r_{L}^{2}/( {2( {r_{L}^{2} + x^{2}} )^{\frac{3}{2}}} )}}} & (20)\end{matrix}$

The receive sensor plus amplifier output voltage, V_(Receive)(t), can begeneralized asV _(Receive)(t)=Gain_(amp)(F _(C))*V _(Rx Sensor)(t)=Gain_(amp)(F_(C))*K _(Rx) *dβ/dt  (21)V _(Receive)(t)=Gain_(amp)(F _(C))*dI _(L)(t)/dt*K _(Rx)*(K_(Tx(#)))  (22)where,

-   -   Gain_(amp)(F_(C))=the amplifier gain at the frequency of        interest    -   K_(Rx)=−n*A*u_(C−Rx) (constant receive terms)    -   n=number of turns in the receive core    -   A=area of the receive core (m²)    -   u_(C−Rx)=geometry dependent relative permeability of the receive        core    -   K_(Tx)(#) is dependent on the source of the time varying        magnetic field        Therefore, an observable asymmetric property in dI_(L)(t)/dt, is        preserved in V_(Receive)(t) The asymmetry may be exploited by        the companion receiver to indicate the direction of approach.

The desired transmit current contains an asymmetry in dI_(L)(t)/dt thatpermits a receiver to determine direction of approach. The dI_(L)(t)/dtasymmetry is observed as a difference between the positive and negativetime duration and/or a difference in the positive and negative peakvalues at the output of the receiver sensor and amplifier chain.

FIG. 7 and FIG. 8 demonstrate excitation characteristics for adominantly inductive wire load. FIGS. 7A-7C show an example of squarewave excitation under an embodiment. FIG. 7A shows load voltage V(t) ofa transmitter as a function of time (seconds). FIG. 7B displays thecorresponding load current. In particular, FIG. 7B shows the filteredload current I_(L) as a function of time (seconds). FIG. 7C shows thefiltered rate of change in load current dI_(L)(t)/dt as a function oftime (seconds). FIGS. 8A-8C shows an example of triangle wave excitationunder an embodiment. FIG. 8A shows the load voltage V(t) of atransmitter as a function of time (seconds). FIG. 8B displays thecorresponding load current. In particular, FIG. 8B shows the filteredload current I_(L) as a function of time (seconds). FIG. 8C shows thefiltered rate of change in load current dI_(L)(t)/dt as a function oftime (seconds). Note from FIG. 7 and FIG. 8 that for dominantlyinductive long wire loads, the desired asymmetry in dI_(L)(t)/dt occursfor square wave excitation.

FIG. 9 and FIG. 10 demonstrate excitation characteristics for adominantly resistive long wire load. FIGS. 9A-9C show an example ofsquare wave excitation under an embodiment. FIG. 9A shows load voltageV(t) of a transmitter as a function of time (seconds). FIG. 9B displaysthe corresponding load current. In particular, FIG. 9B shows thefiltered load current I_(L) as a function of time (seconds). FIG. 9Cshows the filtered rate of change in load current dI_(L)(t)/dt as afunction of time (seconds). FIGS. 10A-10C show an example of trianglewave excitation under an embodiment. FIG. 10A shows the load voltageV(t) of a transmitter as a function of time (seconds). FIG. 10B displaysthe corresponding load current. In particular, FIG. 10B shows thefiltered load current I_(L) as a function of time (seconds). FIG. 10Cshows the filtered rate of change in load current dI_(L)(t)/dt as afunction of time (seconds). Note from FIG. 9 and FIG. 10 that fordominantly resistive long wire loads, the desired asymmetry indI_(L)(t)/dt occurs for asymmetric triangle wave excitation.

System, Method, and Apparatus for Constructing Voltage ExcitationWaveform

Discrete Time Function

Under one embodiment, a discrete time function, I_(L)(nΔt) is createdwhich describes the desired load current asymmetry. Under an embodiment,the desired asymmetry is a triangle current waveform with differentpositive and negative slopes. FIG. 11 shows reference current I_(L)(t)resulting from the discrete time function I_(L)(nΔt) as furtherdescribed below.

OOK (On Off Keying) or amplitude modulation (amplitude shift keying) isused to modulate (or impart data onto) the discrete time functionI_(L)(nΔt) as further described below. The modulation function isreferred to as modulation(nΔt) and resolves to either one or zero underan embodiment.

Rotating phasor values, expressed as Φ(nΔt)=ωnΔt (modulo 2π), are usedto generate the discrete time function I_(L)(nΔt) as further describedbelow.

The discrete time function I_(L)(nΔt) comprises a desired asymmetry of30%. Symmetry test thresholds for Φ(nΔt) are as follows:

s₁=0.942478 radians

s₂=5.340708 radians

Using these test thresholds, the region of positive slope comprises 30%of 2π radians.

FIG. 12 shows phasor Φ(nΔt) rotating about a unit circle with afrequency, f. Note that angular frequency ω (rads/sec)=2πf. FIG. 12shows symmetry test threshold s₁=0.942478 and s₂=5.340708. FIG. 12displays a region of positive slope 1210 and a region of negative slope1220 that result in the desired asymmetry.

The desired positive slope m₁ of I_(L)(nΔt) comprises change inamplitude/change in Φ(nΔt). The desired positive slope of i_(L)(nΔt) ism₁=2/(2*s₁). The desired negative slope m₂ of I_(L)(nΔt) compriseschange in amplitude/change in Φ(nΔt). The desired negative slope ofI_(L)(nΔt) is m₂=−2/(2π−2*s₁).

The discrete time function, I_(L)(nΔt) is given by the following logic:if (modulation(nΔt)!=0)  (23)

-   -   if (Φ(nΔt)>=s₂ OR Φ(nΔt)<s₁), // region of positive slope        -   if (Φ(nΔt)<s₁), ΔΦ=Φ(nΔt)+s₁        -   else ΔΦ=Φ(nΔt)−s₂        -   I_(L)(nΔt)=(modulation(nΔt)*ΔΦ*m₁)−1        -   else // region of negative slope,            ΔΦ=Φ(nΔt)−s ₁        -   I_(L)(nΔt)=(modulation(nΔt)*ΔΦ*m₂)+1

else I_(L)(nΔt)=0 // no modulation

FIG. 13 shows the frequency content of the desired current provided bythe discrete time function, I_(L)(nΔt), when f=20,000 Hz. FIG. 13provides the results of Discrete Fourier Transform analysis. The figureshows a first harmonic at a frequency of 20,000 Hz and with relativeamplitude 53 db. The figure shows a second harmonic at a frequency of40,000 Hz and with relative amplitude of 43 db. The figure shows a thirdharmonic at a frequency of 60,000 Hz and with relative amplitude of 30db. The relative harmonic relationships of the desired I_(L)(nΔt) are:

Harmonic: Relative Amplitude: Relative Phase (rads): 1st 1 0 2nd 0.30600 3rd 0.0819 0Practical limitations of the DFT algorithm permit showing only the firstthree harmonics. In practice, the harmonics continue indefinitely.Approximate Current Using First and Second Harmonics

The desired current may then be approximated using only the first andsecond harmonics. FIG. 14 shows a first carrier I_(FC)(nΔt) component ofthe desired current using the first relative amplitude of the firstharmonic. FIG. 15 shows a second carrier I_(2FC)(nΔt) component of thedesired current using the relative amplitude of the second harmonic.Again note that the relative amplitude of the first and second harmonicsare 1.00 and 0.3060 respectively. Therefore, a two carrier approximationto (nΔt) (shown in FIG. 16) is given byAI _(L)(nΔt)=sin(ωnΔt)+0.3060*sin(2ωnΔt)  (24)

where,

f=20,000 Hz

ω=2πf

The sample rate, 1/Δt, is left to the discretion of the system designerbut should be high enough (i.e. =>8× the fundamental frequency) toachieve the desired precision. The sampling rate used in this example is160,000 Hz, i.e. 8*f. With only two terms, the operations required torealize the approximation are easy to perform in a low cost commercialmicroprocessor using either batch or real time processing algorithms.

Iterative, Adaptive, Feedback Control Algorithm

Derive an Estimate of the Loop Inductance (L_(Loop)) and Loop Resistance(R_(Loop))

Under one embodiment, an estimate of the loop inductance (L_(Loop)) andloop resistance (R_(Loop)) are derived. Reference is made to thetransmit circuit shown in FIG. 1. The transmit circuit of FIG. 1 isexcited with a reference step and the response V_(C)(t) is analyzed.FIG. 17 shows voltage amplitudes V_(out) [˜2V] and V_(C) [˜0.75V] as afunction of time(seconds).

$\begin{matrix}{{V_{C}( {{final}\mspace{14mu}{value}} )} = {{V_{Out}( {{final}\mspace{14mu}{value}} )} = {R_{Sense}/( {R_{Sense} + R_{Loop} + R_{Series}} )}}} & (25) \\{\mspace{79mu}{R_{Loop} = {{( \frac{V_{Out}}{V_{C}} )*R_{Sense}} - R_{Sense} - R_{Series}}}} & (26)\end{matrix}$

For a long wire circuit employed under the embodiment described herein,the R_(series) is in the range of 90-180 ohms and R_(sense) is 30 ohms.

Averaging multiple measurements yields a good approximation of R_(Loop)under an embodiment. The transmit loop time constant may be used toapproximate the value of L_(Loop). The transmit loop time constant maybe expressed as T_(C)=L/R. In one time constant T_(C)=L/R), V_(C)(t)reaches 63.2% of its final value. Under an embodiment, the elapsed time,Δt1, is recorded when V_(C)(t) reaches 63.2% of its final value. In twotime constants, V_(C)(t) reaches 86.5% of its final value. Under anembodiment, the elapsed time, Δt2, is recorded when V_(C)(t) reaches86.5% of its final value. L_(Loop) is calculated as follows:L _(Loop) =R _(Circuit) *Δt1  (27)L _(Loop) =R _(circuit) *Δt2/2  (28)where R_(Circuit)=R_(series)+R_(sense)+R_(Loop). Averaging multiplemeasurements yields a good approximation of L_(Loop).

The measurement interval can be long (as compared to the intervalbetween data transmissions) and left to the discretion of the systemdesigner. In general, changes in the loop parameters (other than an opencircuit) do not occur suddenly. Open circuits can be detected byobserving V_(C)(t) during all other active periods.

Scale the Approximation AI_(L)(nΔt) and Calculate First Iteration ofV_(Gen)(nΔt).

A working animal containment system requires a minimum receive signal ata distance x from the transmit loop. Under an embodiment, the necessaryamplitude of the two carrier approximation, AI_(L)(nΔt) is calculated.V _(Receive-required)=Gaiu_(sensor+amp)(F _(C),2F _(C))*V_(Sensor-required)  (29)V _(Receive-required)=Gaiu_(sensor+amp)(F _(C),2F _(C))*ΔI _(L) /Δt_(-required) *K _(Rx) *KT _(x(#))  (30)ΔI _(L) /Δt _(-required) =V _(Receive-required)/(Gaiu_(sensor+amp)(F_(C),2F _(C))*K _(Rx) *K _(Tx(#)))  (31)where,

-   -   Gain_(senor+amp)(F_(C), 2_(FC))=sensor plus amplifier gain at        the frequency or band of interest.    -   K_(Rx)=−n*A*u_(C−Rx)    -   K_(Tx(#))=is dependent on the distance, x, and the source type¹    -   Δ=the discrete time differentiation operator ¹It is either        K_(Tx-long wire), K_(Tx-coil air), or K_(Tx-coil ferrite).        Under the embodiment described below,

V_(Receive-required)˜18.6 mVRMS

Gain_(sensor+amp)(F_(C), 2F_(C))˜2550

n˜950

A˜1.164e−5 square meters

u_((c−Rx))˜5.523

The sensor plus amplifier needs to be responsive from F_(C) to 2F_(C). Arelatively flat response is ideal, but other response characteristics(gain and phase) may be compensated for by digital signal processing inthe receiver's microprocessor.

Under an embodiment, solve for the load current scaling factor, K_(I):ΔI _(L) /Δt _(-required) =K _(I) *ΔAI _(L) /Δt _(-peak)  (32)K _(I) =ΔI _(L) /Δt _(-required)/(ΔAI _(L) /Δt _(-peak)).  (33)The resulting loop current is therefore,AI_(L)(nΔt)=K_(I)*(sin(ωnΔt)+0.3060*sin(2ωnΔt)). Under an embodiment,V_(Gen)(nΔt) is calculated using Kirchhoff s law, i.e. byV _(Gen)(nΔt)=K ^(I)*(R _(Circuit) *AI _(L)(nΔt)+L _(Loop) *ΔAI_(L)(nΔt)/Δt)).  (34)Under one embodiment the first iteration of the signal generator voltagewaveform, V_(Gen)(nΔt), may be employed as the generator signal forsystem operation. One may stop here if there is high confidence theestimated loop parameters adequately reflect the circuit operatingconditions for achieving the desired amplitude and asymmetry.Observe V_(C)(nΔt) for the Desired Characteristics in the Transmit LoopCurrent AI_(L)(nΔt)

Under an embodiment, one may observe V_(C)(nΔt) for the desiredcharacteristics in the transmit loop current AI_(L) (nΔt). FIG. 18 showsthe same transmit circuit as displayed in FIG. 1 with additionalelements to model the receiver signal processing using V_(C)(nΔt). Asseen in FIG. 18, the V_(C)(nΔt) signal outputs to a digital component130 that approximates the Receiver (Rx) Sensor Response. The digitalapproximation is sufficiently modeled as a single pole high pass filter(f_(corner)=2525 Hz) followed by a single pole low pass filter(f_(corner)=38870 Hz) and a gain of 2550. As seen in FIG. 18, thedigital approximation component 130 outputs to the Receiver (Rx)Detection Component/Algorithm 132. The receiver detectioncomponent/algorithm generates the weighted and time shifted sum of twobandpass filter outputs. One centered at the fundamental carrierfrequency and one centered at 2× the fundamental carrier frequency. Arelative time shift between the two filter outputs is required to matchthe difference in group delay through each bandpass filter. The receiverdetection algorithm (also referred to as the feedback detectionalgorithm) estimates the root means square, V_(Rx-Rms) 134 (at therequired distance measured in Analog-to-Digital-Converter counts) and RxAsymmetry Value 136 (ratio of the aggregate negative to positive signalpeaks) of the receive signal.

Under one embodiment, an adaptive feedback algorithm seeks a solution tosatisfy both the minimum receive signal, V_(Receive)(nΔt), and thedesired receive asymmetry. In this illustrative example, the desiredreceive asymmetry will be the ratio of the aggregate positive andaggregate negative peaks of V_(Receive)(nΔt)

The two frequency transmit current, AI_(L)(nΔt), can be derived from theobserved V_(C)(nΔt) and R_(Sense).AI _(L)(nΔt)=V _(C)(nΔt)/R _(Sense)  (35)ΔAI _(L)(nΔt)/Δt=[ΔAI _(L)(nΔt)−ΔAI _(L)(nΔ(t−1))]/Δt.  (36)

The illustrative example that follows is for a long wire (approximately2500 ft. of 16AWG wire, at an operating frequency of 25000 Hz), where:Δβ/Δt=ΔAI _(L)(nΔt)/Δt*(u ₀/2πx)  (37)where, x=3 meters.

The receive sensor plus amplifier output voltage, V_(Receive)(t), can begeneralized as

$\begin{matrix}{{V_{Receive}(t)} = {{{{Gain}_{amp}( F_{C} )}*V_{Rx}{{Sensor}(t)}} = {{{Gain}_{amp}( F_{C} )}*K_{Rx}*d\;{\beta/{dt}}}}} & (38) \\{\mspace{79mu}{{V_{Receive}(t)} = {{{Gain}_{amp}( F_{C} )}*\frac{{dAI}_{L}( {n\;\Delta\; t} )}{\Delta\; t}*K_{Rx}*( K_{{Tx}{(\#)}} )}}} & (39)\end{matrix}$where,

Gain_(amp)(F_(C))=the amplifier gain at the frequency of interest

K_(Rx)=−n*A*u_(C−Rx) (constant receive terms)

n=number of turns in the receive core

A=area of the receive core (m²)

u_(C−Rx)=geometry dependent relative permeability of the receive core

K_(Tx(#)) is dependent on the source of the time varying magnetic fieldFirst, the load parameters are estimated by the previously describedanalysis of V_(C)(nΔt) when applying a step waveform. FIG. 19 shows astep waveform V_(GEN)(nΔt) reaching voltage of approximately 0.44 volts.FIG. 20 shows the corresponding signal V_(C)(t) reaching a voltage ofapproximately 1.4 volts.

R_(LOOP) and R_(CIRCUIT) values are then estimated as follows.

R_(Loop estimate)=17.568 Ω

L_(Loop estimate)=0.001382 H

R_(circuit)=R_(Series)+R_(Sense)+R_(Loop estimate)=195.393

L_(Circuit)=L_(Loop estimate)=0.001382 H

Under one embodiment, an iterative examination of V_(GEN)(nΔt) beginswith feedback algorithm goals as follows.V _(Rx-RMS) _((at required distance measured in A/D Converter counts))=7.619+/−6.5%Rx AsymmetryRatio_((ratio of the aggregate negative to positive signal peaks))=1.692+/−8.55%The signal generator transmit provides the initial V_(Gen-0)(NΔt) signalto a transmit circuit comprising starting point circuit parameters of aniterative adaptive feedback algorithm. The starting point circuitparameters, Z(0), under an embodiment are:R _(Circuit)=195.393 ΩL _(Loop)=0.001382 H

FIG. 21 shows the initial impedance vector Z(0).

FIG. 22 showsV_(Gen-0)(nΔt)=K_(I)*(R_(Circuit)*AI_(L)(nΔt)+L_(Loop)*ΔAI_(L)(nΔt)/Δt)).

The feedback detection algorithm (see FIG. 18) produces the followingreceive model output results for V_(Gen-0)(nΔt):V _(Rx-Rms) estimate=8.571Rx Asymmetry estimate=1.519

The receive signal RMS is not within the acceptable range under anembodiment. When the RMS is not within limits, a scalar gain adjustmentis needed. The feedback algorithm will scale the circuit impedancevector accordingly. The scalar gain adjustment is described as follows:Scalar gain adjustment:Z=ωL+RZ(n)=Z(n−1)*V _(Rx-RMS goal) /V _(Rx-RMS estimate)

for this example:R _(Circuit)(1)=195.393Ω*7.619/8.571=173.690 ΩL _(Loop)(1)=0.001382H*7.619/8.571=0.0012285H=0.001229HUnder an embodiment, the previously iterated circuit parameters are now:R _(Circuit)=173.6901L _(Loop)=0.001229 HFIG. 23 shows a graph of the impedance vector Z(1).

The V_(Gen-1)(nΔt) signal is then applied to the transmit circuit, whereV_(Gen-1)(nΔt)=K_(I)*(R_(Circuit)*AI_(L)(nΔt)+L_(Loop)*ΔAI_(L)(nΔt)/Δt)).

The feedback detection algorithm produces the following receive modeloutput results for V_(Gen-1)(nΔt):V _(Rx-Rms) estimate=7.546Rx Asymmetry estimate=1.532The receive signal asymmetry is not within the acceptable range under anembodiment. When no gain adjustment is required and the asymmetry is notwithin limits, an impedance vector rotation is needed. The firstrotation in an iteration sequence is assumed to be positive. Thefeedback algorithm will rotate the circuit impedance vector accordingly.

The Z(1) impedance vector has an angle of 48.01 degrees. There is nocorrelation between the asymmetry error and the proper rotationdirection. Our first rotation is assumed to be positive and we rotateone-sixth (⅙) of the degrees between our current angle and 90 degrees.Hence we rotate Z(1) by 7 degrees. The new impedance vector shall havethe same magnitude but at an angle of 55.01 degrees.R(2)=Z(1)Magnitude*cosine(55.01 degrees)ωL(2)=Z(1)Magnitude*sine(55.01 degrees)therefore;L(2)=ωL(2)/ω.Note that there is nothing sacred about rotating ⅙ of the degreesbetween the current angle and the hard boundary (0 or 90 degrees). It isa compromise between the number of iterations required to achieve asuitable end result, and the precision of the end result.

Under an embodiment, the previously iterated circuit parameters are now:R _(circuit)=148.884 ΩL _(Loop)=0.001354HFIG. 24 shows a graph of the impedance vector Z(2).

The V_(Gen-2)(nΔt) signal is then applied to the transmit circuit, whereV_(Gen-2)(nΔt)=K_(I)*(R_(circuit)*AI_(L)(nΔt)+L_(Loop)*ΔAI_(L)(nΔt)/Δt)).

The feedback detection algorithm produces the following receive modeloutput results for V_(Gen-2)(nΔt):V _(Rx-Rms) estimate=7.546Rx Asymmetry estimate=1.532The receive signal asymmetry is not within the acceptable range under anembodiment. When no gain adjustment is required and the asymmetry is notwithin limits, an impedance vector rotation is needed. Positive rotationdid not improve the asymmetry. Therefore, a negative rotation is used.The feedback algorithm will rotate the circuit impedance vectoraccordingly.

The Z(2) impedance vector has an angle of 55.01 degrees. Our firstrotation was assumed to be positive. It did not improve the asymmetryresult, therefore we must rotate in the negative direction. Rotateone-sixth (⅙) of the degrees between our current angle and 0 degrees.Hence we rotate Z(2) by 9.71 degrees. The new impedance vector shallhave the same magnitude but at an angle of 45.84 degrees.R(3)=Z(2) Magnitude*cosine(45.84 degrees)ωL(3)=Z(2) Magnitude*sine(45.84 degrees)therefore;L(3)=ωL(3)/ω

Under an embodiment, the previously iterated circuit parameters are now:R _(circuit)=180.872 ΩL _(Loop)=0.001186HFIG. 25 shows a graph of the impedance vector Z(3).

The V_(Gen-3)(nΔt) signal is then applied to the transmit circuit, whereV_(Gen-3)(nΔt)=K_(I)*(R_(Circuit)*AI_(L)(nΔt)+L_(Loop)*ΔAI_(L)(nΔt)/Δt)).The feedback detection algorithm produces the following receive modeloutput results for V_(Gen-3)(nΔt):V _(Rx-Rms) estimate=7.7092Rx Asymmetry estimate=1.582The receive signal RMS and asymmetry are within acceptable ranges. Theadaptive feedback algorithm is complete under an embodiment. The correctcircuit parameters for normal operation are:R _(circuit)=180.872L _(Loop)=0.001186HAlso notice that the circuit impedance vector for the 3^(rd) and finaliteration is neither predominantly inductive or resistive. Therefore,the required V_(Gen-3)(nΔt) is neither an “uneven duty cycle squarewave” nor a “triangle wave with adjustable slopes”.

A method is described herein that comprises describing a load currentwith a discrete time function. The method includes using a firstfrequency and a second frequency to provide an approximation of thedescribed load current, wherein a transform applied to the discrete timefunction identifies the first frequency and the second frequency. Themethod includes estimating a loop inductance and a loop resistance of awire loop by exciting a transmit circuit with a voltage reference stepwaveform, wherein the transmit circuit includes the wire loop. Themethod includes scaling the approximated load current to a levelsufficient to generate a minimum receive voltage signal in a receiver ata first distance between the wire loop and the receiver. The methodincludes generating a first voltage signal using the scaled loadcurrent, the estimated loop inductance, and the estimated loopresistance. The method includes exciting the transmit circuit with thefirst voltage signal.

The estimating the loop inductance and the loop resistance includesunder an embodiment monitoring the transmit circuit's current inresponse to the voltage reference step waveform.

The monitoring the transmit circuit's current includes under anembodiment capturing current amplitude as a function of time in responseto the voltage reference step waveform.

The transform comprises a Discrete Fourier Transform under anembodiment. The first frequency comprises a first harmonic frequency ofthe described load current under an embodiment.

The second frequency comprises a second harmonic frequency of thedescribed load current under an embodiment.

The method comprises under an embodiment generating a first carriercomponent of the approximated load current using the first harmonicfrequency, wherein the first carrier component has a weight of one.

The method comprises under an embodiment generating a second carriercomponent of the approximated load current using the second harmonicfrequency, wherein an amplitude of the second carrier component isweighted relative to an amplitude of the first carrier component.

The transform applied to the discrete time function used to describe theload current identifies under an embodiment the relative weight of thesecond carrier component.

The providing the approximation of the described load current includessumming the first carrier component and the second carrier componentunder an embodiment.

The approximated load current comprises a discrete time function underan embodiment.

The first voltage signal comprises a discrete time function under anembodiment.

An input to the discrete time function used to describe the load currentcomprises a rotating phasor under an embodiment.

The phasor value periodically rotates between 0 and 27c radians under anembodiment.

The discrete time function used to describe the load current has a firstslope when the phasor value is within a first range under an embodiment.

The first slope is positive under an embodiment.

The discrete time function used to describe the load current has asecond slope when the phasor value is within a second range under anembodiment.

The second slope is negative under an embodiment.

The first range comprises approximately thirty percent of 2π radiansunder an embodiment.

The absolute value of the first slope is greater than the absolute valueof the second slope under an embodiment.

The method comprises under an embodiment reading a voltage signal at alocation in the transmit circuit, wherein the voltage signal isrepresentative of a corresponding transmit current in the transmitcircuit.

The method comprises under an embodiment processing the voltage signalto estimate the receive voltage signal.

The estimating includes under an embodiment determining a root meansquare (RMS) of the estimated receive voltage signal.

The estimating includes under an embodiment determining an asymmetry ofthe estimated receive voltage signal.

The asymmetry comprises under an embodiment a ratio of the aggregatepositive and aggregate negative peaks of the estimated receive voltagesignal.

The method comprises establishing a target RMS value under anembodiment.

A target RMS range comprises under an embodiment he target RMS valueplus or minus a percentage.

The method of an embodiment comprises establishing a target asymmetryvalue.

A target asymmetry range comprises under an embodiment the targetasymmetry value plus or minus a percentage.

The method under an embodiment comprises iteratively adjusting animpedance vector of the transmit circuit until the RMS and the asymmetryof estimated receive voltage signal fall within the corresponding targetRMS and asymmetry ranges, wherein the impedance vector initiallycomprises the loop resistance and the loop inductance.

The adjusting comprises under an embodiment scaling the impedance vectorwhen the RMS falls outside the target RMS range.

The adjusting comprises under an embodiment rotating a phase angle ofthe impedance vector when the asymmetry falls outside the targetasymmetry range.

The rotating the phase angle comprising under an embodiment a negativerotation.

The rotating the phase angle comprises under an embodiment a positiverotation.

The described load current comprises an asymmetry under an embodiment.

The receiver exploits under an embodiment the asymmetry to determine thereceiver's direction of approach to the wire loop carrying the describedload current.

Computer networks suitable for use with the embodiments described hereininclude local area networks (LAN), wide area networks (WAN), Internet,or other connection services and network variations such as the worldwide web, the public internet, a private internet, a private computernetwork, a public network, a mobile network, a cellular network, avalue-added network, and the like. Computing devices coupled orconnected to the network may be any microprocessor controlled devicethat permits access to the network, including terminal devices, such aspersonal computers, workstations, servers, mini computers, main-framecomputers, laptop computers, mobile computers, palm top computers, handheld computers, mobile phones, TV set-top boxes, or combinationsthereof. The computer network may include one or more LANs, WANs,Internets, and computers. The computers may serve as servers, clients,or a combination thereof.

The apparatus, systems and methods for generating voltage excitationwaveforms can be a component of a single system, multiple systems,and/or geographically separate systems. The apparatus, systems andmethods for generating voltage excitation waveforms can also be asubcomponent or subsystem of a single system, multiple systems, and/orgeographically separate systems. The components of the apparatus,systems and methods for generating voltage excitation waveforms can becoupled to one or more other components (not shown) of a host system ora system coupled to the host system.

One or more components of the apparatus, systems and methods forgenerating voltage excitation waveforms and/or a correspondinginterface, system or application to which the apparatus, systems andmethods for generating voltage excitation waveforms is coupled orconnected includes and/or runs under and/or in association with aprocessing system. The processing system includes any collection ofprocessor-based devices or computing devices operating together, orcomponents of processing systems or devices, as is known in the art. Forexample, the processing system can include one or more of a portablecomputer, portable communication device operating in a communicationnetwork, and/or a network server. The portable computer can be any of anumber and/or combination of devices selected from among personalcomputers, personal digital assistants, portable computing devices, andportable communication devices, but is not so limited. The processingsystem can include components within a larger computer system.

The processing system of an embodiment includes at least one processorand at least one memory device or subsystem. The processing system canalso include or be coupled to at least one database. The term“processor” as generally used herein refers to any logic processingunit, such as one or more central processing units (CPUs), digitalsignal processors (DSPs), application-specific integrated circuits(ASIC), etc. The processor and memory can be monolithically integratedonto a single chip, distributed among a number of chips or components,and/or provided by some combination of algorithms. The methods describedherein can be implemented in one or more of software algorithm(s),programs, firmware, hardware, components, circuitry, in any combination.

The components of any system that include the apparatus, systems andmethods for generating voltage excitation waveforms can be locatedtogether or in separate locations. Communication paths couple thecomponents and include any medium for communicating or transferringfiles among the components. The communication paths include wirelessconnections, wired connections, and hybrid wireless/wired connections.The communication paths also include couplings or connections tonetworks including local area networks (LANs), metropolitan areanetworks (MANs), wide area networks (WANs), proprietary networks,interoffice or backend networks, and the Internet. Furthermore, thecommunication paths include removable fixed mediums like floppy disks,hard disk drives, and CD-ROM disks, as well as flash RAM, UniversalSerial Bus (USB) connections, RS-232 connections, telephone lines,buses, and electronic mail messages.

Aspects of the apparatus, systems and methods for generating voltageexcitation waveforms and corresponding systems and methods describedherein may be implemented as functionality programmed into any of avariety of circuitry, including programmable logic devices (PLDs), suchas field programmable gate arrays (FPGAs), programmable array logic(PAL) devices, electrically programmable logic and memory devices andstandard cell-based devices, as well as application specific integratedcircuits (ASICs). Some other possibilities for implementing aspects ofthe apparatus, systems and methods for generating voltage excitationwaveforms and corresponding systems and methods include:microcontrollers with memory (such as electronically erasableprogrammable read only memory (EEPROM)), embedded microprocessors,firmware, software, etc. Furthermore, aspects of the apparatus, systemsand methods for generating voltage excitation waveforms andcorresponding systems and methods may be embodied in microprocessorshaving software-based circuit emulation, discrete logic (sequential andcombinatorial), custom devices, fuzzy (neural) logic, quantum devices,and hybrids of any of the above device types. Of course the underlyingdevice technologies may be provided in a variety of component types,e.g., metal-oxide semiconductor field-effect transistor (MOSFET)technologies like complementary metal-oxide semiconductor (CMOS),bipolar technologies like emitter-coupled logic (ECL), polymertechnologies (e.g., silicon-conjugated polymer and metal-conjugatedpolymer-metal structures), mixed analog and digital, etc.

It should be noted that any system, method, and/or other componentsdisclosed herein may be described using computer aided design tools andexpressed (or represented), as data and/or instructions embodied invarious computer-readable media, in terms of their behavioral, registertransfer, logic component, transistor, layout geometries, and/or othercharacteristics. Computer-readable media in which such formatted dataand/or instructions may be embodied include, but are not limited to,non-volatile storage media in various forms (e.g., optical, magnetic orsemiconductor storage media) and carrier waves that may be used totransfer such formatted data and/or instructions through wireless,optical, or wired signaling media or any combination thereof. Examplesof transfers of such formatted data and/or instructions by carrier wavesinclude, but are not limited to, transfers (uploads, downloads, e-mail,etc.) over the Internet and/or other computer networks via one or moredata transfer protocols (e.g., HTTP, FTP, SMTP, etc.). When receivedwithin a computer system via one or more computer-readable media, suchdata and/or instruction-based expressions of the above describedcomponents may be processed by a processing entity (e.g., one or moreprocessors) within the computer system in conjunction with execution ofone or more other computer programs.

Unless the context clearly requires otherwise, throughout thedescription and the claims, the words “comprise,” “comprising,” and thelike are to be construed in an inclusive sense as opposed to anexclusive or exhaustive sense; that is to say, in a sense of “including,but not limited to.” Words using the singular or plural number alsoinclude the plural or singular number respectively. Additionally, thewords “herein,” “hereunder,” “above,” “below,” and words of similarimport, when used in this application, refer to this application as awhole and not to any particular portions of this application. When theword “or” is used in reference to a list of two or more items, that wordcovers all of the following interpretations of the word: any of theitems in the list, all of the items in the list and any combination ofthe items in the list.

The above description of embodiments of the apparatus, systems andmethods for generating voltage excitation waveforms is not intended tobe exhaustive or to limit the systems and methods to the precise formsdisclosed. While specific embodiments of, and examples for, theapparatus, systems and methods for generating voltage excitationwaveforms and corresponding systems and methods are described herein forillustrative purposes, various equivalent modifications are possiblewithin the scope of the systems and methods, as those skilled in therelevant art will recognize. The teachings of the apparatus, systems andmethods for generating voltage excitation waveforms and correspondingsystems and methods provided herein can be applied to other systems andmethods, not only for the systems and methods described above.

The elements and acts of the various embodiments described above can becombined to provide further embodiments. These and other changes can bemade to the apparatus, systems and methods for generating voltageexcitation waveforms and corresponding systems and methods in light ofthe above detailed description.

We claim:
 1. A method comprising, one or more applications running on atleast one processor for providing, describing a load current with adiscrete time function, wherein an input to the discrete time functionused to describe the load current comprises a rotating phasor; using afirst frequency and a second frequency to provide an approximation ofthe described load current, wherein a transform applied to the discretetime function identifies the first frequency and the second frequency;estimating a loop inductance and a loop resistance of a wire loop byexciting a transmit circuit with a voltage reference step waveform,wherein the transmit circuit includes the wire loop; scaling theapproximated load current to a level sufficient to generate a minimumreceive voltage signal in a receiver at a first distance between thewire loop and the receiver; generating a first voltage signal using thescaled load current, the estimated loop inductance, and the estimatedloop resistance; exciting the transmit circuit with the first voltagesignal.
 2. The method of claim 1, wherein the estimating the loopinductance and the loop resistance includes monitoring the transmitcircuit's current in response to the voltage reference step waveform. 3.The method of claim 2, wherein the monitoring the transmit circuit'scurrent includes capturing current amplitude as a function of time inresponse to the voltage reference step waveform.
 4. The method of claim1, wherein the transform comprises a Discrete Fourier Transform.
 5. Themethod of claim 1, wherein the first frequency comprises a firstharmonic frequency of the described load current.
 6. The method of claim5, wherein the second frequency comprises a second harmonic frequency ofthe described load current.
 7. The method of claim 6, comprisinggenerating a first carrier component of the approximated load currentusing the first harmonic frequency, wherein the first carrier componenthas a weight of one.
 8. The method of claim 7, comprising generating asecond carrier component of the approximated load current using thesecond harmonic frequency, wherein an amplitude of the second carriercomponent is weighted relative to an amplitude of the first carriercomponent.
 9. The method of claim 8, wherein the transform applied tothe discrete time function used to describe the load current identifiesthe relative weight of the second carrier component.
 10. The method ofclaim 8, wherein the providing the approximation of the described loadcurrent includes summing the first carrier component and the secondcarrier component.
 11. The method of claim 1, wherein the approximatedload current comprises a discrete time function.
 12. The method of claim1, wherein the first voltage signal comprises a discrete time function.13. The method of claim 1, wherein the phasor value periodically rotatesbetween 0 and 2π radians.
 14. The method of claim 13, wherein thediscrete time function used to describe the load current has a firstslope when the phasor value is within a first range.
 15. The method ofclaim 14, wherein the first slope is positive.
 16. The method of claim14, wherein the discrete time function used to describe the load currenthas a second slope when the phasor value is within a second range. 17.The method of claim 14, wherein the second slope is negative.
 18. Themethod of claim 14, wherein the first range comprises approximatelythirty percent of 2.pi. radians.
 19. The method of claim 18, wherein theabsolute value of the first slope is greater than the absolute value ofthe second slope.
 20. The method of claim 1, comprising reading avoltage signal at a location in the transmit circuit, wherein thevoltage signal is representative of a corresponding transmit current inthe transmit circuit.
 21. The method of claim 20, comprising processingthe voltage signal to estimate the receive voltage signal.
 22. Themethod of claim 21, the estimating including determining a root meansquare (RMS) of the estimated receive voltage signal.
 23. The method ofclaim 22, the estimating including determining an asymmetry of theestimated receive voltage signal.
 24. The method of claim 23, whereinthe asymmetry comprises a ratio of the aggregate positive and aggregatenegative peaks of the estimated receive voltage signal.
 25. The methodof claim 23, comprising establishing a target RMS value.
 26. The methodof claim 25, wherein a target RMS range comprises the target RMS valueplus or minus a percentage.
 27. The method of claim 26, comprisingestablishing a target asymmetry value.
 28. The method of claim 27,wherein a target asymmetry range comprises the target asymmetry valueplus or minus a percentage.
 29. The method of claim 28, comprisingiteratively adjusting an impedance vector of the transmit circuit untilthe RMS and the asymmetry of estimated receive voltage signal fallwithin the corresponding target RMS and asymmetry ranges, wherein theimpedance vector initially comprises the loop resistance and the loopinductance.
 30. The method of claim 29, the adjusting comprising scalingthe impedance vector when the RMS falls outside the target RMS range.31. The method of claim 29, the adjusting comprising rotating a phaseangle of the impedance vector when the asymmetry falls outside thetarget asymmetry range.
 32. The method of claim 31, the rotating thephase angle comprising a negative rotation.
 33. The method of claim 31,the rotating the phase angle comprising a positive rotation.
 34. Themethod of claim 1, wherein the described load current comprises anasymmetry.
 35. The method of claim 34, wherein the receiver exploits theasymmetry to determine the receiver's direction of approach to the wireloop carrying the described load current.